Question

x²+kx+40. in this equation's ratio of roots is 2:5, than find the value of k​

Answer 1

Answer:

14 or -14

Step-by-step explanation:

since the roots are in the ratio 2:5, let the roots be 2m and 5m

Sum of the roots=-k

⇒2m+5m=-k

⇒7m= -k

⇒m= -k/7

product of the roots=40

⇒2mX5m=40

⇒10m²=40

⇒m²=4

⇒(-k/7)²=4

⇒k²/49=4

⇒k²=49X4

⇒k=±(7X2)=±14

So k can be 14 or -14

Answer 2

           

$\bold{Answer: \ \ \ k=\pm14}$

 

   

$p(x)=x^2+kx+40 \\ \\ \\ a=1\ \ \ ; \ \ \ b=k\ \ \ ; \ \ \ c=40 \\ \\ \\ Let the roots be \ 2\alpha\ and \ 5\alpha. \\ \\ \\ Product of roots \ = c/a \\ \\ \Rightarrow\ 2\alpha \times 5\alpha=40/1 \\ \\ \Rightarrow\ 10\alpha^2=40 \\ \\ \Rightarrow\ \alpha^2=4 \\ \\ \Rightarrow\ \alpha=\pm2 \\ \\ \Rightarrow\ 2\alpha=\pm4 \\ \\ \Rightarrow\ 5\alpha=\pm 10$

$(x-4)(x-10)=x^2+kx+40 \\ \\ \Rightarrow\ x^2-14x+40=x^2+kx+40 \\ \\ \\ \therefore\ k=\bold{-14} \\ \\ \\ OR \\ \\ \\ (x+4)(x+10)=x^2+kx+40 \\ \\ \Rightarrow\ x^2+14x+40=x^2+kx+40 \\ \\ \\ \therefore\ k=\bold{14} \\ \\ \\ \\ \therefore\ k=\bold{\pm14}$

$Hope this helps. Plz ask me if you've any doubts. \\ \\ \\ Thank you. :-))$